Conserved- and zero-mean quadratic quantities in oscillatory systems

P Rapisarda; JC Willems

doi:10.1007/s00498-005-0149-4

Conserved- and zero-mean quadratic quantities in oscillatory systems

P Rapisarda^*, JC Willems

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities. We also state an equipartition of energy principle for oscillatory systems.

Original language	English
Pages (from-to)	173-200
Number of pages	28
Journal	Mathematics of Control Signals and Systems
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s00498-005-0149-4
Publication status	Published - Aug 2005

Keywords

linear oscillatory systems
two-variable polynomial matrices
quadratic differential forms
behavioral system theory
equipartition of energy
DIFFERENTIAL FORMS
INTERCONNECTED SYSTEMS

Access to Document

10.1007/s00498-005-0149-4

Cite this

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title = "Conserved- and zero-mean quadratic quantities in oscillatory systems",

abstract = "We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities. We also state an equipartition of energy principle for oscillatory systems.",

keywords = "linear oscillatory systems, two-variable polynomial matrices, quadratic differential forms, behavioral system theory, equipartition of energy, DIFFERENTIAL FORMS, INTERCONNECTED SYSTEMS",

author = "P Rapisarda and JC Willems",

year = "2005",

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doi = "10.1007/s00498-005-0149-4",

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AU - Rapisarda, P

AU - Willems, JC

PY - 2005/8

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N2 - We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities. We also state an equipartition of energy principle for oscillatory systems.

AB - We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities. We also state an equipartition of energy principle for oscillatory systems.

KW - linear oscillatory systems

KW - two-variable polynomial matrices

KW - quadratic differential forms

KW - behavioral system theory

KW - equipartition of energy

KW - DIFFERENTIAL FORMS

KW - INTERCONNECTED SYSTEMS

U2 - 10.1007/s00498-005-0149-4

DO - 10.1007/s00498-005-0149-4

M3 - Article

SN - 0932-4194

VL - 17

SP - 173

EP - 200

JO - Mathematics of Control Signals and Systems

JF - Mathematics of Control Signals and Systems

IS - 3

ER -